ISWEC (Inertial Sea Wave Energy Converter) is a device which converts wave energy into electricity exploiting the gyroscopic moment of a spinning flywheel. This thesis is part of the design of a gyroscopic unit in which the rotor levitates on a magnetic suspension to reduce the friction losses and hence improve the system efficiency. The work analyzes how to ensure the system mechanical integrity not only in normal operating conditions but also in case of magnetic suspension failure or overload. To achieve this aim, rotor natural frequencies and the corresponding vibration modes are obtained by FEM numerical simulations. It is verified that the rotor does not reach any critical speeds during normal operating conditions.